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September/October 2015 Local well-posedness and blow-up result for weakly dissipative Camassa-Holm equations
Sungyong Park
Adv. Differential Equations 20(9/10): 983-1008 (September/October 2015).

Abstract

In this paper, we consider the Cauchy problem of the weakly dissipative Camassa-Holm equation. We prove the local well-posedness in the critical inhomogeneous Besov space $B^{3/2}_{2,1}( \mathbb R )$. This result depends on the apriori estimate of the nonlinear transport equation. Moreover, we show result for the finite time blowing up solution of the the weakly dissipative Camass-Holm equation which unifies previously known result. The proof relies on geometrical approach for the weakly dissipative Camass-Holm equation.

Citation

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Sungyong Park. "Local well-posedness and blow-up result for weakly dissipative Camassa-Holm equations." Adv. Differential Equations 20 (9/10) 983 - 1008, September/October 2015.

Information

Published: September/October 2015
First available in Project Euclid: 23 June 2015

zbMATH: 1326.35323
MathSciNet: MR3360397

Subjects:
Primary: 35Q53

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.20 • No. 9/10 • September/October 2015
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